In a 1-dimensional problem, a single force acts on a 10 kg object and is given the equation F=ax+b where a=250 N/m, b=25 N, x is position of object. There is a force acting on the object while that object moves from x=0 to x=2 lasting 3 sec.
1) What is the work done by this force during the time interval?
What is the average power developed by this force during the time interval.
If the object was at rest when x=0, what is the kinetic energy of the object at x=2m
.
1. F = 250*2 + 25 = 525 N.
Work = F*d = 525 * 2 = 1050 Joules.
2. P = F*d/t = 525 * 2/3 = 350 J/s. =
350 Watts.
To find the work done by a force, we can use the equation W = F * d, where W represents work, F represents force, and d represents displacement.
In this case, the force acting on the object is given by F = ax + b, where a is 250 N/m and b is 25 N. The object moves from x = 0 to x = 2m, so the displacement is d = 2m - 0m = 2m.
To find the work done, substitute the values into the equation:
W = (ax + b) * d
W = (250 N/m * 2m + 25 N) * 2m
W = (500 N + 25 N) * 2m
W = 525 N * 2m
W = 1050 Nm or 1050 J (Joules)
Therefore, the work done by this force during the time interval is 1050 Joules.
To find the average power developed by this force during the time interval, we can use the equation P = W / t, where P represents power and t represents time.
In this case, the time interval is given as 3 seconds.
Substitute the values into the equation:
P = W / t
P = 1050 J / 3 s
P ≈ 350 W (Watts)
Therefore, the average power developed by this force during the time interval is approximately 350 Watts.
If the object was at rest when x = 0, then the initial velocity (v0) of the object would be zero. We can use the kinematic equation to find the final kinetic energy (KE) of the object at x = 2m:
KE = (1/2) * m * v^2
Given:
m = 10 kg (mass of the object)
x = 2m (displacement)
v0 = 0 m/s (initial velocity)
To find the final velocity (v), we can use the kinematic equation:
v^2 = v0^2 + 2a * d
Substitute the values into the equation:
v^2 = 0^2 + 2a * 2m
v^2 = 4a
v = 2 * sqrt(a)
Now substitute this value of v into the equation for KE:
KE = (1/2) * m * v^2
KE = (1/2) * 10 kg * (2 * sqrt(a))^2
KE = 20 * a
KE = 20 * 250 N/m
KE = 5000 J (Joules)
Therefore, the kinetic energy of the object at x = 2m is 5000 Joules.