A child on a sled is initially at rest on an icy horizontal surface. The sled is pushed until it reaches a final velocity of 7.00 m/s in a distance of 11.2 m. The coefficient of friction between the ice and runners of the sled is 0.200, and the weight of the child and the sled is 360 N. Find the work done by the force pushing the sled.
Well, well, well, looks like we've got a little physics problem on our hands! Let's see if we can slide into a solution, shall we?
First things first, let's talk about the work done by the force pushing the sled. Work, my friend, is defined as the product of the force applied and the distance over which it's applied. In this case, the force pushing the sled is the total force acting on it, which is the sum of the pushing force and the frictional force.
Now, to find the pushing force, we need to consider the frictional force. Since the sled is on an icy surface, we know that the coefficient of friction is 0.200. Remember that the frictional force can be calculated as the coefficient of friction multiplied by the normal force. In this case, the normal force is equal to the weight of the child and the sled, which is 360 N.
So, the frictional force is 0.200 times 360 N, which is 72 N. But hold your sleigh bells, we're not done yet! We also need to find the pushing force, which is responsible for accelerating the sled.
To find the pushing force, we can use Newton's second law which states that force is equal to mass times acceleration. In this case, the mass of the child and the sled doesn't matter because we're only interested in the force. The acceleration can be calculated by using the final velocity, initial velocity (which is 0 since the sled is initially at rest), and the distance traveled. So, the acceleration is equal to the change in velocity divided by the distance, which is 7.00 m/s divided by 11.2 m.
Alright, now that we have the acceleration, we can calculate the pushing force by multiplying the acceleration by the mass. Oops, I mean the pushing force by the weight. And since weight is mass multiplied by the acceleration due to gravity, we can substitute weight with mass multiplied by 9.8 m/s^2. So, the pushing force is equal to the pushing force divided by weight multiplied by weight, which is the pushing force divided by weight times 9.8 m/s^2.
Now that we have the pushing force, we can finally calculate the work done by it. Work is equal to force multiplied by distance. So, the work done by the force pushing the sled is the pushing force multiplied by the distance traveled, which is the pushing force multiplied by 11.2 m.
Phew! That was a slippery slope, but we made it! So, with all that mathematical jargon out of the way, grab your clown nose and your sled, because the work done by the force pushing the sled is equal to... drumroll, please... the pushing force multiplied by the distance traveled, which is the pushing force multiplied by 11.2 m.
To find the work done by the force pushing the sled, we can use the work-energy principle. The work done by a force is equal to the change in kinetic energy. In this case, the initial kinetic energy is zero since the sled is initially at rest.
The final kinetic energy can be calculated using the equation:
Kf = (1/2)mv^2, where Kf is the final kinetic energy, m is the mass, and v is the final velocity.
Since the weight of the child and sled is given, we can find the mass using Newton's second law:
F = ma, where F is the weight (360 N) and a is the acceleration.
Let's calculate the mass:
360 N = m * 9.8 m/s² (acceleration due to gravity)
m = 360 N / 9.8 m/s²
m ≈ 36.73 kg
Now, let's calculate the final kinetic energy:
Kf = (1/2) * 36.73 kg * (7.00 m/s)^2
Kf ≈ 903.89 J
The work done by the force pushing the sled is equal to the change in kinetic energy:
Work = Kf - Ki (initial kinetic energy)
Work = Kf - 0 J (since the initial kinetic energy is zero)
Work = 903.89 J
Therefore, the work done by the force pushing the sled is approximately 903.89 Joules.
To find the work done by the force pushing the sled, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
In this case, the work done by the force pushing the sled will be equal to the change in its kinetic energy. The initial kinetic energy (K_i) is zero since the sled is initially at rest. The final kinetic energy (K_f) can be calculated using the formula K_f = (1/2)mv^2, where m is the mass and v is the final velocity.
To find the mass of the child and sled, we can divide the weight (W) by the acceleration due to gravity (g), using the formula m = W/g.
Given:
Final velocity (v) = 7.00 m/s
Distance (d) = 11.2 m
Coefficient of friction (μ) = 0.200
Weight (W) = 360 N
Acceleration due to gravity (g) = 9.8 m/s^2
First, let's find the mass (m) of the child and sled:
m = W/g = 360 N / 9.8 m/s^2 ≈ 36.7 kg
Now, let's calculate the final kinetic energy (K_f):
K_f = (1/2)mv^2 = (1/2)(36.7 kg)(7.00 m/s)^2 ≈ 903.7 J
Since the initial kinetic energy (K_i) is zero, the work done by the force pushing the sled is equal to the change in kinetic energy:
Work = K_f - K_i = 903.7 J - 0 J = 903.7 J
Therefore, the work done by the force pushing the sled is approximately 903.7 Joules.