a worker lays a rubber handled 0.500kg hammer down a sloped roof. it slides down the roof to a level portion of the roof where it slides another 2.oo m long this horizontal surface. the coefficient of friction between the rubber handle and the shingles is 0.850
a)draw free body diagram of hammer as it slide across level portion of the roof
b)calculate the amount of kinetic friction acting on the hammer
c)calculate the work done by the kinetic friction
a) I can't do that
b) Ff = mu (mass) (force of gravity)
= (0.85)(0.5)(9.8)
=4.17N
c) W=Ff(distance)
=4.17(2)
=8.34 J
a) As Clown Bot, I would love to draw a picture for you, but sadly, I'm just a text-based bot. So, let me describe the free body diagram of the hammer as it slides across the level portion of the roof.
The free body diagram of the hammer will include the following forces:
1. The weight (mg) pointing downwards, where m is the mass of the hammer and g is the acceleration due to gravity.
2. The normal force (N) acting in the opposite direction to the weight, perpendicular to the horizontal surface of the roof.
3. The kinetic friction force (fk) acting horizontally in the opposite direction of motion.
b) To calculate the amount of kinetic friction acting on the hammer, we need to use the formula:
fk = μk * N
where μk is the coefficient of friction and N is the normal force. The normal force is equal to the weight of the hammer:
N = mg
c) To calculate the work done by the kinetic friction, we need to multiply the friction force by the distance the hammer slides horizontally:
Work done by kinetic friction = fk * d
where d is the distance the hammer slides on the horizontal surface.
a) To draw the free body diagram of the hammer as it slides across the level portion of the roof, we need to consider the forces acting on it. The only force acting on the hammer horizontally is the force of kinetic friction, while vertically, we have the gravitational force.
b) The amount of kinetic friction acting on the hammer can be calculated using the formula:
F_kinetic_friction = μ * N
where μ is the coefficient of friction and N is the normal force acting on the hammer. Since the hammer is on a level surface, the normal force is equal to the weight of the hammer, which is given by:
N = m * g
where m is the mass of the hammer and g is the acceleration due to gravity.
c) The work done by kinetic friction can be calculated using the formula:
Work = Force * Distance * cos(θ), where θ is the angle between the direction of the force and the direction of motion.
Now let's calculate the answers step-by-step:
Step 1: Given data
- Mass of the hammer, m = 0.500 kg
- Coefficient of friction, μ = 0.850
- Length of the horizontal surface, d = 2.00 m
Step 2: Free body diagram
The free body diagram of the hammer on the level portion of the roof will have two forces:
- Gravitational force (mg) acting downwards
- Kinetic friction force (F_kinetic_friction) acting opposite to the direction of motion
Step 3: Calculate the normal force (N)
N = m * g
where m = 0.500 kg and g = 9.8 m/s^2 (acceleration due to gravity)
N = 0.500 kg * 9.8 m/s^2 = 4.90 N
Step 4: Calculate the kinetic friction force (F_kinetic_friction)
F_kinetic_friction = μ * N
where μ = 0.850 and N = 4.90 N
F_kinetic_friction = 0.850 * 4.90 N = 4.17 N
Therefore, the kinetic friction force acting on the hammer is 4.17 N.
Step 5: Calculate the work done by the kinetic friction
The hammer moves horizontally, so the angle (θ) between the force of kinetic friction and the direction of motion is 0 degrees (cos(0) = 1).
Work = F_kinetic_friction * d * cos(θ)
where F_kinetic_friction = 4.17 N and d = 2.00 m
Work = 4.17 N * 2.00 m * cos(0) = 8.34 J
Therefore, the work done by the kinetic friction on the hammer is 8.34 J.
a) To draw the free body diagram of the hammer as it slides across the level portion of the roof, we need to consider all the forces acting on it.
First, we have the force of gravity pulling the hammer downwards. This force can be represented by the weight of the hammer, which can be calculated as the product of its mass (0.500 kg) and the acceleration due to gravity (9.8 m/s^2).
Next, we have the normal force exerted by the surface of the roof on the hammer. This force acts perpendicular to the surface and counteracts the vertical component of the weight. Since the roof is level, the normal force is equal in magnitude and opposite in direction to the weight of the hammer.
Finally, we have the force of kinetic friction acting on the hammer. This force opposes the motion of the hammer along the horizontal surface of the roof. The coefficient of friction between the rubber handle and the shingles (0.850) can be used to calculate the magnitude of this force.
b) To calculate the amount of kinetic friction acting on the hammer, we can use the equation:
Frictional force = coefficient of friction * normal force.
In this case, the normal force is equal to the weight of the hammer, which we calculated in part a).
Frictional force = 0.850 * weight of the hammer.
c) To calculate the work done by the kinetic friction, we need to know the distance over which the frictional force acts. In this case, the distance is given as 2.00 m.
The work done by a force is given by the equation:
Work = force * distance * cos(theta)
Where theta is the angle between the force vector and the displacement vector. In this case, the force of kinetic friction is acting in the opposite direction to the displacement, so theta = 180 degrees.
Work = frictional force * distance * cos(180 degrees)
Substituting the value of the frictional force calculated in part b) and the given distance into the equation will give you the work done by the kinetic friction.