QuestionA powerful motorcycle can produce an acceleration of $3.50 \mathrm{~m} / \mathrm{s}^{2}$ while traveling at $90.0 \mathrm{~km} / \mathrm{h}$ . At that speed, the forces resisting motion, including frictio and air resistance, total 400.0 N . (Air resistance is analogous to air friction. It always opposes the motion of an object.) What is the magnitude of the fo that motorcycle exerts backward on the.ground to produce its acceleration if the mass of the motorcycle with rider is 245 kg ?

Studdy Solution

STEP 1

1. The motorcycle is accelerating at $3.50 \, \mathrm{m/s}^2$ .
2. The resisting forces total $400.0 \, \mathrm{N}$ .
3. The mass of the motorcycle with the rider is $245 \, \mathrm{kg}$ .
4. The net force is calculated using Newton's second law of motion.

STEP 2

1. Recall Newton's second law of motion.
2. Calculate the net force required for the given acceleration.
3. Determine the total force exerted by the motorcycle.
4. Calculate the magnitude of the force the motorcycle exerts backward on the ground.

STEP 3

Recall Newton's second law of motion:
$F_{\text{net}} = m \cdot a$
where $F_{\text{net}}$ is the net force, $m$ is the mass, and $a$ is the acceleration.

STEP 4

Calculate the net force required for the given acceleration:
$F_{\text{net}} = 245 \, \mathrm{kg} \times 3.50 \, \mathrm{m/s}^2$
$F_{\text{net}} = 857.5 \, \mathrm{N}$

STEP 5

Determine the total force exerted by the motorcycle. The total force exerted by the motorcycle must overcome the resisting forces and provide the net force for acceleration:
$F_{\text{total}} = F_{\text{net}} + F_{\text{resisting}}$
$F_{\text{total}} = 857.5 \, \mathrm{N} + 400.0 \, \mathrm{N}$

STEP 6

Calculate the magnitude of the force the motorcycle exerts backward on the ground:
$F_{\text{total}} = 857.5 \, \mathrm{N} + 400.0 \, \mathrm{N}$
$F_{\text{total}} = 1257.5 \, \mathrm{N}$
The magnitude of the force that the motorcycle exerts backward on the ground is:
$\boxed{1257.5 \, \mathrm{N}}$

Was this helpful?

Studdy Solution

STEP 1

1. The motorcycle is accelerating at $3.50 \, \mathrm{m/s}^2$ .
2. The resisting forces total $400.0 \, \mathrm{N}$ .
3. The mass of the motorcycle with the rider is $245 \, \mathrm{kg}$ .
4. The net force is calculated using Newton's second law of motion.

STEP 2

1. Recall Newton's second law of motion.
2. Calculate the net force required for the given acceleration.
3. Determine the total force exerted by the motorcycle.
4. Calculate the magnitude of the force the motorcycle exerts backward on the ground.

STEP 3

Recall Newton's second law of motion:
$F_{\text{net}} = m \cdot a$
where $F_{\text{net}}$ is the net force, $m$ is the mass, and $a$ is the acceleration.

STEP 4

Calculate the net force required for the given acceleration:
$F_{\text{net}} = 245 \, \mathrm{kg} \times 3.50 \, \mathrm{m/s}^2$
$F_{\text{net}} = 857.5 \, \mathrm{N}$

STEP 5

Determine the total force exerted by the motorcycle. The total force exerted by the motorcycle must overcome the resisting forces and provide the net force for acceleration:
$F_{\text{total}} = F_{\text{net}} + F_{\text{resisting}}$
$F_{\text{total}} = 857.5 \, \mathrm{N} + 400.0 \, \mathrm{N}$

STEP 6

Calculate the magnitude of the force the motorcycle exerts backward on the ground:
$F_{\text{total}} = 857.5 \, \mathrm{N} + 400.0 \, \mathrm{N}$
$F_{\text{total}} = 1257.5 \, \mathrm{N}$
The magnitude of the force that the motorcycle exerts backward on the ground is:
$\boxed{1257.5 \, \mathrm{N}}$

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.

Studdy Solution

STEP 1

1. The motorcycle is accelerating at 3.50 m/s23.50 \, \mathrm{m/s}^23.50m/s2.2. The resisting forces total 400.0 N400.0 \, \mathrm{N}400.0N.3. The mass of the motorcycle with the rider is 245 kg245 \, \mathrm{kg}245kg.4. The net force is calculated using Newton's second law of motion.

STEP 2

1. Recall Newton's second law of motion.2. Calculate the net force required for the given acceleration.3. Determine the total force exerted by the motorcycle.4. Calculate the magnitude of the force the motorcycle exerts backward on the ground.

STEP 3

Recall Newton's second law of motion:Fnet=m⋅a F_{\text{net}} = m \cdot a Fnet​=m⋅awhere Fnet F_{\text{net}} Fnet​ is the net force, m m m is the mass, and a a a is the acceleration.

STEP 4

Calculate the net force required for the given acceleration:Fnet=245 kg×3.50 m/s2 F_{\text{net}} = 245 \, \mathrm{kg} \times 3.50 \, \mathrm{m/s}^2 Fnet​=245kg×3.50m/s2Fnet=857.5 N F_{\text{net}} = 857.5 \, \mathrm{N} Fnet​=857.5N

STEP 5

STEP 6

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.

1. The motorcycle is accelerating at $3.50 \, \mathrm{m/s}^2$ .
2. The resisting forces total $400.0 \, \mathrm{N}$ .
3. The mass of the motorcycle with the rider is $245 \, \mathrm{kg}$ .
4. The net force is calculated using Newton's second law of motion.

1. Recall Newton's second law of motion.
2. Calculate the net force required for the given acceleration.
3. Determine the total force exerted by the motorcycle.
4. Calculate the magnitude of the force the motorcycle exerts backward on the ground.

Recall Newton's second law of motion:
$F_{\text{net}} = m \cdot a$
where $F_{\text{net}}$ is the net force, $m$ is the mass, and $a$ is the acceleration.

Calculate the net force required for the given acceleration:
$F_{\text{net}} = 245 \, \mathrm{kg} \times 3.50 \, \mathrm{m/s}^2$
$F_{\text{net}} = 857.5 \, \mathrm{N}$