A 45 kg trunk is pushed 7.8 m at constant speed up a 30° incline by a constant horizontal force. The coefficient of kinetic friction between the trunk and the incline is 0.23.
a)Calculate the work done by the applied horizontal force.
b)Calculate the work done by the weight of the trunk.
c)How much energy was dissipated by the frictional force acting on the trunk?
I found a to be 2773.4 J and b to be -1719.9 J but i cannot get c at all. Im not even sure what equation to use.
c. energyinfriction= frictionforce*distance
= 45gCos30*mu*7.8 Joules
To find the energy dissipated by the frictional force acting on the trunk, you can use the following equation:
c) Energy Dissipated = Work done by the Frictional Force
To calculate the work done by the frictional force, you need to know the magnitude of the frictional force.
To find the magnitude of the frictional force, you can use the equation:
Frictional Force = coefficient of kinetic friction * Normal Force,
where the Normal Force is the component of the weight of the trunk that is perpendicular to the incline. It is given by:
Normal Force = Weight * cosθ,
where θ is the angle of the incline.
Let's calculate the magnitude of the frictional force first:
Weight = mass * gravitational acceleration
= 45 kg * 9.8 m/s²
= 441 N
Normal Force = Weight * cosθ
= 441 N * cos(30°)
= 382.59 N
Frictional Force = coefficient of kinetic friction * Normal Force
= 0.23 * 382.59 N
= 88.22 N
Now, we can calculate the work done by the frictional force using the formula:
Work done = Magnitude of Force * Distance * cos(180°),
where the Magnitude of Force is the magnitude of frictional force, and the Distance is the distance the trunk is pushed.
c) Energy Dissipated = Work done by the Frictional Force
= (-Magnitude of Force) * Distance * cos(180°)
= (-88.22 N) * 7.8 m * cos(180°)
= -680.28 J
So, the energy dissipated by the frictional force acting on the trunk is -680.28 J. It is negative because the force acts opposite to the direction of displacement.
To solve part c), you need to calculate the work done by the frictional force acting on the trunk. The work done by a force can be calculated using the equation:
Work = Force x Distance x Cosθ
Where:
- Work is the amount of energy transferred or dissipated
- Force is the force applied or acting on the object
- Distance is the displacement of the object
- θ is the angle between the force and the direction of displacement
In this scenario, the force causing the work done by friction is the force of friction. The force of friction can be calculated using the equation:
Force of Friction = Coefficient of Friction x Normal Force
Where:
- Coefficient of Friction is the value given in the problem (0.23)
- Normal Force is the force perpendicular to the incline, which is equal to the weight of the trunk in this case (mass x gravity)
Given:
- Mass (m) of the trunk = 45 kg
- Incline angle (θ) = 30 degrees
- Distance (d) the trunk is pushed = 7.8 m
- Coefficient of Kinetic Friction (μ) = 0.23
To calculate the normal force (N), you can use:
Normal Force = Weight of the Trunk
Weight of the Trunk = mg
Where:
- m is the mass of the trunk (45 kg)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Let's calculate step by step:
Step 1: Calculate the normal force (N):
Weight of the Trunk = mass x acceleration due to gravity
Weight of the Trunk = 45 kg x 9.8 m/s^2
N = 441 N
Step 2: Calculate the force of friction (Ff):
Force of Friction = Coefficient of Friction x Normal Force
Ff = 0.23 x 441 N
Ff = 101.43 N
Step 3: Calculate the work done by friction:
Work = Force x Distance x Cosθ
Work = Ff x d x Cosθ
Work = 101.43 N x 7.8 m x Cos(30°)
Work ≈ 665.0 J
Therefore, the energy dissipated by the frictional force acting on the trunk is approximately 665.0 Joules (J).