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QuestionA 2.0 kg2.0 \mathrm{~kg} object on a bench is connected to a 3.0 kg3.0 \mathrm{~kg} object via a pulley. It accelerates at 4.0 m/s24.0 \mathrm{~m/s}^2.
(a) Find the resultant force on the 2.0 kg2.0 \mathrm{~kg} object: force= \text{force} =
(b) Determine the upward force FF on the 3.0 kg3.0 \mathrm{~kg} object: force F= \text{force } F =

Studdy Solution

STEP 1

Assumptions1. The mass of the first object is .0 kg.0 \mathrm{~kg} . The mass of the second object is 3.0 kg3.0 \mathrm{~kg}
3. The acceleration of the first object is 4.0 m/s4.0 \mathrm{~m} / \mathrm{s}^{}
4. The force acting on the first object is the resultant force5. The upward force exerted by the cord on the second object is $$
6. The acceleration due to gravity is $9.8 \mathrm{~m} / \mathrm{s}^{}$

STEP 2

First, we need to find the resultant force acting on the 2.0 kg2.0 \mathrm{~kg} object. We can do this by using Newton's second law of motion, which states that force equals mass times acceleration.
Force=MasstimesAccelerationForce = Mass \\times Acceleration

STEP 3

Now, plug in the given values for the mass and acceleration of the first object to calculate the force.
Force=2.0 kgtimes.0 m/s2Force =2.0 \mathrm{~kg} \\times.0 \mathrm{~m} / \mathrm{s}^{2}

STEP 4

Calculate the resultant force acting on the 2.0 kg2.0 \mathrm{~kg} object.
Force=2.0 kgtimes4.0 m/s2=8.0 Force =2.0 \mathrm{~kg} \\times4.0 \mathrm{~m} / \mathrm{s}^{2} =8.0 \mathrm{~}

STEP 5

Now, we need to find the upward force $$ exerted by the cord on the $3.0 \mathrm{~kg}$ object. We can do this by using the equation for the force of gravity, which is mass times the acceleration due to gravity, and then subtracting this from the force exerted by the first object.
=Force−(MasstimesGravity) = Force - (Mass \\times Gravity)

STEP 6

Now, plug in the given values for the force, mass of the second object, and acceleration due to gravity to calculate $$.
=8.0 −(3.0 kgtimes9.8 m/s2) =8.0 \mathrm{~} - (3.0 \mathrm{~kg} \\times9.8 \mathrm{~m} / \mathrm{s}^{2})

STEP 7

Calculate the upward force $$ exerted by the cord on the $3.0 \mathrm{~kg}$ object.
=.0 −(3.0 kgtimes9. m/s2)=−21.4  =.0 \mathrm{~} - (3.0 \mathrm{~kg} \\times9. \mathrm{~m} / \mathrm{s}^{2}) = -21.4 \mathrm{~}The negative sign indicates that the force is acting in the opposite direction, i.e., downward.
So, the resultant force acting on the 2.0 kg2.0 \mathrm{~kg} object is .0 .0 \mathrm{~} and the upward force $$ exerted by the cord on the $3.0 \mathrm{~kg}$ object is $-21.4 \mathrm{~}$.

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