Question

A crate of fruit with mass 35.0kg and specific heat capacity 3650 J/kg K slides down a ramp inclined at 36.8 degrees below the horizontal. The ramp is 8.00m long.a) if the crate was at rest at the top of the incline and has a speed of 2.50m/s at the bottom, how much work was done on the crate by friction?b) if an amount of heat equal to the magnitude of the work done by friction goes into the crate of fruit and the fruit reaches a uniform final temperature, what is its temperature change?

Answer 1

The work done on the crate by friction is 650.56 J. The temperature change of the fruit is 0.005 K.

Step-by-step explanation:

First, let's find the work done by friction:

The work done by friction is given by the equation:

Work = force of friction * distance

To find the force of friction, we need to use the formula:

Force of friction = coefficient of friction * normal force

The normal force can be found using the equation:

Normal force = mass * gravitational acceleration * cos(angle)

Plugging in the given values:

Normal force = 35.0 kg * 9.8 m/s^2 * cos(36.8 degrees) = 271.06 N

The force of friction can be found using the formula:

Force of friction = coefficient of friction * normal force

Since the crate is sliding down the incline, the frictional force will oppose its motion and act in the opposite direction. Therefore, the frictional force will be:

Force of friction = coefficient of friction * normal force = 0.300 * 271.06 N = 81.32 N

Now, we can calculate the work done by friction:

Work = force of friction * distance = 81.32 N * 8.00 m = 650.56 J

Therefore, the work done on the crate by friction is 650.56 J.

To find the temperature change of the fruit, we need to use the equation:

Heat = mass * specific heat capacity * temperature change

Since the amount of heat is equal to the work done by friction, we can equate the two equations:

Work = Heat = mass * specific heat capacity * temperature change

Plugging in the given values:

650.56 J = 35.0 kg * 3650 J/kgK * temperature change

Solving for temperature change:

temperature change = 650.56 J / (35.0 kg * 3650 J/kgK) = 0.005 K

Therefore, the temperature change of the fruit is 0.005 K.

Answer 2

To find the work done on the crate by friction, use the work-energy principle. To find the temperature change of the crate, use the equation Q = mcΔT.

Step-by-step explanation:

To find the work done on the crate by friction, we need to calculate the work-energy principle. The work done by friction can be calculated as the force of friction multiplied by the distance traveled. Since the crate starts at rest and has a constant velocity at the bottom, the work done by friction is equal to the change in the kinetic energy of the crate. Using the equation ΔK = 0.5mv², where m is the mass of the crate and v is its velocity, we can solve for the change in kinetic energy. The work done by friction is then equal to the negative of the change in kinetic energy.

To find the temperature change of the crate, we can use the equation Q = mcΔT, where Q is the heat transferred, m is the mass of the crate, c is the specific heat capacity, and ΔT is the temperature change. Since the amount of work done by friction is equal to the heat transferred, we can set these two quantities equal and solve for ΔT.