Question

a truck is pulling an 85-kg rock attached by a rope. the coefficient of friction between the rock and the ground is 0.32. the truck applies 295 n of force to the rock. determine the net force and the acceleration.​

Answer 1

The net force acting on the rock is 28.89 N, and the acceleration of the rock is 0.34 m/s^2.

Step-by-step explanation:

Net Force:

To determine the net force acting on the rock, subtract the force of friction from the applied force. The force of friction can be found by multiplying the coefficient of friction by the normal force, which is equal to the weight of the rock. The weight of the rock can be calculated by multiplying its mass by the acceleration due to gravity. Therefore, the net force is equal to the applied force minus the force of friction.

Acceleration:

To find the acceleration of the rock, divide the net force by the mass of the rock. So, the acceleration is equal to the net force divided by the mass of the rock.

Given that the coefficient of friction is 0.32, the force applied by the truck is 295 N, and the mass of the rock is 85 kg, we can calculate the net force and acceleration as follows:
Net Force = Applied Force - Force of Friction

Force of Friction = Coefficient of Friction * Normal Force

Net Force = 295 N - (0.32 * (85 kg * 9.8 m/s^2))

Net Force = 295 N - (0.32 * 833.6 N)

Net Force = 295 N - 266.11 N

Net Force = 28.89 N

Acceleration = Net Force / Mass

Acceleration = 28.89 N / 85 kg

Acceleration = 0.34 m/s^2

Therefore, the net force acting on the rock is 28.89 N and the acceleration of the rock is 0.34 m/s^2.

Answer 2

Net Force = 28.44 N

Acceleration = 0.33
`(m)/(s^2)`

Step-by-step explanation:

First, solve for the force of friction:

`f=\mu N`

For this problem, let

`\mu` = 0.32

`N=mg\\N=(85\ kg)(9.8\ (m)/(s^2))\\N=833\ N`

So, the force of friction can be calculated as

`f=(0.32)(833\ N)\\f=266.56\ N`

Because the force of friction opposes the motion, the net force can be found by subtracting the force of friction from the force applied by the truck.

`F_t=F_T-F_N`

`F_t=295\ N\\F_N=266.56\ N\\F_t=295\ N-266.56\ N\\F_t=28.44\ N`

Finally, rearrange Newton's second law of motion (F=ma) to find the rock's acceleration:

`a=(F_t)/(m)\\a=(28.44\ N)/(85\ kg)\\a=0.33\ (m)/(s^2)`