A 30 kg child slides down a playground slide at a constant speed. The slide has a height of 3.8m and is 7.8m long. using energy considerations, find the magnitude of the kinetic friction force acting on the child.
To find the magnitude of the kinetic friction force acting on the child, we can use energy considerations.
Step 1: Calculate the gravitational potential energy (GPE) of the child at the top of the slide using the formula:
GPE = mass * gravity * height
where mass = 30 kg, gravity = 9.8 m/s^2, and height = 3.8 m.
GPE = 30 kg * 9.8 m/s^2 * 3.8 m
GPE = 1117.6 J
Step 2: Calculate the work done by the friction force using the formula:
Friction force * distance = GPE
where distance = 7.8 m (the length of the slide).
Friction force * 7.8 m = 1117.6 J
Step 3: Rearrange the equation to solve for the friction force:
Friction force = GPE / distance
Friction force = 1117.6 J / 7.8 m
Friction force ≈ 143.1 N
So, the magnitude of the kinetic friction force acting on the child is approximately 143.1 N.
To find the magnitude of the kinetic friction force acting on the child, we can use energy considerations.
1. First, let's calculate the potential energy of the child at the top of the slide. The potential energy is given by the formula P.E. = mgh, where m is the mass (30 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the slide (3.8 m).
P.E. = (30 kg) * (9.8 m/s^2) * (3.8 m)
P.E. = 1122.6 Joules
2. Next, let's calculate the kinetic energy of the child at the bottom of the slide. The kinetic energy is given by the formula K.E. = (1/2)mv^2, where m is the mass (30 kg) and v is the velocity of the child at the bottom of the slide.
Since the child slides down at a constant speed, the velocity at the bottom of the slide will be the same as the velocity at the top of the slide. Therefore, v = 0 m/s.
K.E. = (1/2) * (30 kg) * (0 m/s)^2
K.E. = 0 Joules
3. Now, let's consider the work done by the friction force. The work done is given by the formula W = Fd, where F is the force of friction and d is the distance over which the friction force acts.
The work done by the friction force is equal to the decrease in mechanical energy, which is the initial potential energy minus the final kinetic energy.
W = P.E. - K.E.
W = 1122.6 J - 0 J
W = 1122.6 J
4. We know the distance over which the friction force acts is the length of the slide (7.8 m).
W = Fd
1122.6 J = F * 7.8 m
Now we can solve for the magnitude of the kinetic friction force (F).
F = 1122.6 J / 7.8 m
F ≈ 143.9 N
Therefore, the magnitude of the kinetic friction force acting on the child is approximately 143.9 Newtons.
Since the KE does not change, the work done by gravity equals that done by friction. Thus the friction force times the distance slid equals the change in potential energy m g h
m g h = F * 7.8