1.)A ball (m 0.5 kg) starts from rest and has 300 J(joule) of work applied to it.
a) what is the initial kinetic energy of the ball?
b) what is the final kinetic of the ball?
c) what is the final velocity of the ball?
2.)A boy is doing chin-up. If the boy does 450 N of work to lift his body 0.25 m.
a) how much work does the boy do to lift himself up?
b) if he starts from rest, what his final kinetic energy?
c) what is the boy's final velocity?
>> FORMULAS <<
W= Fd
KE=1/2 v^2
PE= mgm
kg.m/s^2.m
kg.m^2/s^2=J
im sorry i don't know which formula to use. please help me! :)
a) KE₀=0
b) KE= 300 J
c) v=sqrt(2•KE/m)=…(m/s)
2)
a)W=mgh=450•0.25 = ... J
b) KE(fin) =0
c) v=0
No problem, I can help you with that! To solve these problems, we'll need to use a few formulas related to work, kinetic energy, and velocity.
1) For the first question, we'll use the work-energy theorem and the formula for kinetic energy:
a) The initial kinetic energy (KE) of an object can be calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity. Since the ball starts from rest, its initial velocity (V0) is 0, so the initial kinetic energy is also 0.
b) The final kinetic energy can be found using the formula W = ΔKE, where W is the work done on the object and ΔKE is the change in kinetic energy. In this case, the work done on the ball is given as 300 J, so the final kinetic energy is also 300 J.
c) To find the final velocity (v), we can rearrange the formula for kinetic energy as v = √(2 * KE / m). Plugging in the values, we get v = √(2 * 300 J / 0.5 kg), which simplifies to v = √(600 J / 0.5 kg) = √(1200 m^2/s^2 / 0.5 kg) = √(2400 m^2/s^2 / kg) = √(2400) = 48.99 m/s (rounded to two decimal places).
2) For the second question:
a) The work done by the boy to lift himself up is given as 450 N. Since work (W) is equal to force (F) multiplied by distance (d), we can calculate the distance using the formula W = F * d. Rearranging the formula, we get d = W / F = 450 N * 0.25 m = 112.5 J.
b) Assuming no energy is lost to other factors such as friction, the work done by the boy to lift himself up results in an equal increase in his kinetic energy. Therefore, the final kinetic energy is equal to the work done, which is 112.5 J.
c) To find the final velocity of the boy, we can use the formula v = √(2 * KE / m), just like in the first question. Plugging in the values, we get v = √(2 * 112.5 J / m), but since the mass (m) of the boy is not given, we cannot determine the final velocity without that information.
I hope this helps! Let me know if you have any further questions.