Question3
Fig. 2.1 shows a wooden trolley of mass 1.2 kg at rest on the rough surface of a bench.
Fig. 2.1 A ball of mass 0.52 g travels horizontally towards the trolley. The ball embeds itself in the wood of the trolley. The trolley moves with an initial speed of $0.065 \mathrm{~m} / \mathrm{s}$ . (a) Calculate: (i) the impulse exerted on the trolley impulse $=$ $\qquad$ [2] (ii) the speed of the ball as it hits the trolley. speed $=$ $\qquad$ [2]

Studdy Solution

STEP 1

What is this asking? We need to find the impulse on the trolley and the initial speed of the ball before it hit the trolley. Watch out! The masses are in different units!
Also, remember that the ball sticks to the trolley.

STEP 2

1. Convert Units
2. Calculate the Impulse
3. Calculate the Ball's Initial Speed

STEP 3

Alright, let's convert those pesky units!
We've got kilograms and grams, and we want everything in the same units to avoid confusion.
Let's convert the ball's mass to kilograms.
We know that $1 \text{ kg} = 1000 \text{ g}$ , so we can divide the ball's mass in grams by $\textbf{1000}$ to get its mass in kilograms.

STEP 4

So, the ball's mass is $ 0.52 \text{ g} \cdot \frac{1 \text{ kg}}{1000 \text{ g}} = \textbf{0.00052 kg}$.
Awesome!

STEP 5

Now, let's talk impulse!
Impulse is the change in momentum.
Since the trolley started at rest, its initial momentum was $\textbf{zero}$ .
The final momentum is just the mass of the combined trolley and ball multiplied by their final velocity.

STEP 6

The combined mass is $1.2 \text{ kg} + 0.00052 \text{ kg} = \textbf{1.20052 kg}$ .
The final velocity is given as $\textbf{0.065 m/s}$ .
So, the final momentum is $1.20052 \text{ kg} \cdot 0.065 \text{ m/s} = \textbf{0.0780338 kg} \cdot \text{m/s}$ .

STEP 7

Since the initial momentum was zero, the change in momentum, which is the impulse, is just the final momentum: $\textbf{0.078 kg} \cdot \text{m/s}$ (rounded to two significant figures).
Boom!

STEP 8

Time to find the ball's initial speed!
We'll use the principle of conservation of momentum.
The total momentum before the collision must equal the total momentum after the collision.

STEP 9

Before the collision, the trolley was at rest, so its momentum was $\textbf{zero}$ .
The ball's momentum was its mass ( $0.00052 \text{ kg}$ ) times its initial speed (which we'll call $v$ ).
So, the total initial momentum was just $0.00052 \text{ kg} \cdot v$ .

STEP 10

We already calculated the final momentum: $0.0780338 \text{ kg} \cdot \text{m/s}$ .
Now we can set up our equation: $0.00052 \text{ kg} \cdot v = 0.0780338 \text{ kg} \cdot \text{m/s}$ .

STEP 11

To solve for $v$ , we divide both sides of the equation by $0.00052 \text{ kg}$ : $v = \frac{0.0780338 \text{ kg} \cdot \text{m/s}}{0.00052 \text{ kg}}$ $v \approx \textbf{150 m/s}$ That ball was fast!

STEP 12

The impulse exerted on the trolley is $0.078 \text{ kg} \cdot \text{m/s}$ .
The speed of the ball as it hits the trolley is approximately $150 \text{ m/s}$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the impulse on the trolley and the initial speed of the ball before it hit the trolley. Watch out! The masses are in different units!
Also, remember that the ball sticks to the trolley.

STEP 2

1. Convert Units
2. Calculate the Impulse
3. Calculate the Ball's Initial Speed

STEP 3

STEP 4

So, the ball's mass is \( 0.52 \text{ g} \cdot \frac{1 \text{ kg}}{1000 \text{ g}} = \textbf{0.00052 kg}\).
Awesome!

STEP 5

Now, let's talk impulse!
Impulse is the change in momentum.
Since the trolley started at rest, its initial momentum was $\textbf{zero}$ .
The final momentum is just the mass of the combined trolley and ball multiplied by their final velocity.

STEP 6

The combined mass is $1.2 \text{ kg} + 0.00052 \text{ kg} = \textbf{1.20052 kg}$ .
The final velocity is given as $\textbf{0.065 m/s}$ .
So, the final momentum is $1.20052 \text{ kg} \cdot 0.065 \text{ m/s} = \textbf{0.0780338 kg} \cdot \text{m/s}$ .

STEP 7

Since the initial momentum was zero, the change in momentum, which is the impulse, is just the final momentum: $\textbf{0.078 kg} \cdot \text{m/s}$ (rounded to two significant figures).
Boom!

STEP 8

Time to find the ball's initial speed!
We'll use the principle of conservation of momentum.
The total momentum before the collision must equal the total momentum after the collision.

STEP 9

Before the collision, the trolley was at rest, so its momentum was $\textbf{zero}$ .
The ball's momentum was its mass ( $0.00052 \text{ kg}$ ) times its initial speed (which we'll call $v$ ).
So, the total initial momentum was just $0.00052 \text{ kg} \cdot v$ .

STEP 10

We already calculated the final momentum: $0.0780338 \text{ kg} \cdot \text{m/s}$ .
Now we can set up our equation: $0.00052 \text{ kg} \cdot v = 0.0780338 \text{ kg} \cdot \text{m/s}$ .

STEP 11

To solve for $v$ , we divide both sides of the equation by $0.00052 \text{ kg}$ : $v = \frac{0.0780338 \text{ kg} \cdot \text{m/s}}{0.00052 \text{ kg}}$ $v \approx \textbf{150 m/s}$ That ball was fast!

STEP 12

The impulse exerted on the trolley is $0.078 \text{ kg} \cdot \text{m/s}$ .
The speed of the ball as it hits the trolley is approximately $150 \text{ m/s}$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the *impulse* on the trolley and the *initial speed* of the ball before it hit the trolley. Watch out! The masses are in different units!Also, remember that the ball *sticks* to the trolley.

STEP 2

1. Convert Units2. Calculate the Impulse3. Calculate the Ball's Initial Speed

STEP 3

STEP 4

So, the ball's mass is \( 0.52 \text{ g} \cdot \frac{1 \text{ kg}}{1000 \text{ g}} = \textbf{0.00052 kg}\).Awesome!

STEP 5

Now, let's talk **impulse**!Impulse is the *change* in momentum.Since the trolley started at rest, its initial momentum was zero\textbf{zero}zero.The final momentum is just the mass of the *combined* trolley and ball multiplied by their **final velocity**.

STEP 6

STEP 7

Since the initial momentum was zero, the *change* in momentum, which is the impulse, is just the final momentum: 0.078 kg⋅m/s\textbf{0.078 kg} \cdot \text{m/s}0.078 kg⋅m/s (rounded to two significant figures).Boom!

STEP 8

Time to find the ball's **initial speed**!We'll use the principle of *conservation of momentum*.The total momentum *before* the collision must equal the total momentum *after* the collision.

STEP 9

STEP 10

We already calculated the *final* momentum: 0.0780338 kg⋅m/s0.0780338 \text{ kg} \cdot \text{m/s}0.0780338 kg⋅m/s.Now we can set up our equation: 0.00052 kg⋅v=0.0780338 kg⋅m/s0.00052 \text{ kg} \cdot v = 0.0780338 \text{ kg} \cdot \text{m/s}0.00052 kg⋅v=0.0780338 kg⋅m/s.

STEP 11

STEP 12

The impulse exerted on the trolley is 0.078 kg⋅m/s0.078 \text{ kg} \cdot \text{m/s}0.078 kg⋅m/s.The speed of the ball as it hits the trolley is approximately 150 m/s150 \text{ m/s}150 m/s.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to find the impulse on the trolley and the initial speed of the ball before it hit the trolley. Watch out! The masses are in different units!
Also, remember that the ball sticks to the trolley.

1. Convert Units
2. Calculate the Impulse
3. Calculate the Ball's Initial Speed

So, the ball's mass is \( 0.52 \text{ g} \cdot \frac{1 \text{ kg}}{1000 \text{ g}} = \textbf{0.00052 kg}\).
Awesome!

Now, let's talk impulse!
Impulse is the change in momentum.
Since the trolley started at rest, its initial momentum was $\textbf{zero}$ .
The final momentum is just the mass of the combined trolley and ball multiplied by their final velocity.

Since the initial momentum was zero, the change in momentum, which is the impulse, is just the final momentum: $\textbf{0.078 kg} \cdot \text{m/s}$ (rounded to two significant figures).
Boom!

Time to find the ball's initial speed!
We'll use the principle of conservation of momentum.
The total momentum before the collision must equal the total momentum after the collision.

We already calculated the final momentum: $0.0780338 \text{ kg} \cdot \text{m/s}$ .
Now we can set up our equation: $0.00052 \text{ kg} \cdot v = 0.0780338 \text{ kg} \cdot \text{m/s}$ .

The impulse exerted on the trolley is $0.078 \text{ kg} \cdot \text{m/s}$ .
The speed of the ball as it hits the trolley is approximately $150 \text{ m/s}$ .