Question

A 7.00 kg package slides 3.30 m down a long ramp that is inclined at 24.0∘ below the horizontal. The coefficient of kinetic friction between the package and the ramp is 0.310.

What is the work done on the package by friction?

Answer 1

To find the work done on the package by friction, we need to calculate the frictional force acting on the package and multiply it by the distance the package slides down the ramp.

1. First, let's calculate the frictional force using the formula:

Frictional force = coefficient of friction * Normal force

The normal force is the perpendicular force exerted by the ramp on the package. It can be calculated as:

Normal force = mass * gravity * cos(angle of inclination)

Plugging in the given values, we have:

Normal force = 7.00 kg * 9.8 m/s^2 * cos(24.0∘)

2. Now that we have the normal force, we can calculate the frictional force:

Frictional force = 0.310 * Normal force

3. Finally, to find the work done on the package by friction, we multiply the frictional force by the distance the package slides down the ramp:

Work done by friction = Frictional force * distance

Work done by friction = Frictional force * 3.30 m

By following these steps, you should be able to calculate the work done on the package by friction. Remember to use the correct units and plug in the given values accurately to obtain an accurate answer.

Answer 2

Answer: 67.523 J

Step-by-step explanation:

To calculate the work done on the package by friction, we need to use the formula:

Work = Force * Distance * cos(theta)

First, let's find the force of friction. The force of friction can be calculated using the formula:

Force of friction = coefficient of friction * normal force

The normal force is the force exerted perpendicular to the surface of the ramp. In this case, it is equal to the weight of the package, which is given by:

Weight = mass * gravity

Plugging in the values, we have:

Weight = 7.00 kg * 9.8 m/s^2 = 68.6 N

Next, we can find the force of friction:

Force of friction = 0.310 * 68.6 N = 21.266 N

Now, let's calculate the distance. The distance the package slides down the ramp is given as 3.30 m.

Finally, we need to find the angle between the force of friction and the direction of motion. In this case, the angle is 24.0 degrees below the horizontal. Since the force of friction acts opposite to the direction of motion, we subtract 180 degrees from 24 degrees to get 156 degrees.

Now, we can calculate the work done by friction:

Work = 21.266 N * 3.30 m * cos(156 degrees)

Make sure to convert the angle to radians when using the cosine function.

Work = 21.266 N * 3.30 m * cos(156 degrees) = -67.523 J

The negative sign indicates that the work done by friction is in the opposite direction of the motion of the package.