A child whose weight is 281 N slides down a 6.20 m playground slide that makes an angle of 45.0¡ã with the horizontal. The coefficient of kinetic friction between slide and child is 0.160. (a) How much energy is transferred to thermal energy? (b) If she starts at the top with a speed of 0.516 m/s, what is her speed at the bottom?
N=mgcos@=281cos45
Ffr = u * N = .16 * 281cos45
Wfr = Ffr*d = Ffr * 6.2
Work done by friction is the energy transfered to thermal, and is your change in total energy.
Thus for part b, E0 = mgh + mv^2/2
at the botto she has E0 - Wfr total energy and it is all kinetic.
From there do the algebra and sub in numbers.
To find the answers to these questions, we need to use principles of physics. Let's break down the problem step by step.
(a) How much energy is transferred to thermal energy?
To find the amount of energy transferred to thermal energy, we need to calculate the work done by friction. The work done by friction can be found using the formula:
Work done by friction = frictional force * distance
The frictional force can be calculated using the formula:
Frictional force = coefficient of kinetic friction * normal force
where the normal force is the vertical component of the weight, which can be calculated as:
Normal force = weight * cos(angle)
In this case, the weight of the child is given as 281 N and the angle of the slide is 45 degrees.
Hence, we can calculate the normal force as:
Normal force = 281 N * cos(45 degrees)
Once we have the normal force, we can find the frictional force using the coefficient of kinetic friction.
Next, we can calculate the work done by friction as the product of the frictional force and the distance (6.20 m) the child slides down the slide.
Finally, the energy transferred to thermal energy is equal to the work done by friction.
(b) If she starts at the top with a speed of 0.516 m/s, what is her speed at the bottom?
To calculate the speed at the bottom of the slide, we need to consider the conservation of mechanical energy. Initially, the child has gravitational potential energy, which is converted to kinetic energy at the bottom of the slide.
The gravitational potential energy at the starting point can be calculated as:
Gravitational potential energy = weight * height
where the height of the slide is given as 6.20 m.
At the bottom of the slide, this potential energy is converted into kinetic energy, which can be expressed as:
Kinetic energy = (1/2) * mass * velocity^2
where the mass can be calculated using the weight and the acceleration due to gravity, and the velocity can be found using the law of conservation of mechanical energy.
Finally, we can solve for the velocity at the bottom of the slide.
By following these steps and performing the necessary calculations, we can find the answers to both (a) and (b) of the question.