A 15 N force is needed to move an object with constant velocity of 5 m/s. What power must be delivered to the object by the force?
I konw that P=W/t
and W=Fd
But other than that I am confused . I am not sure how i would solve this problem.
power= W/t= force*distane/time= force*velocty
To solve this problem, we can use the formula for power. Power (P) is defined as the work done (W) per unit time (t). We can calculate the work done by multiplying the force applied (F) to move the object by the displacement (d) of the object. The work done can be represented as W = Fd.
Given:
Force (F) = 15 N
Velocity (v) = 5 m/s
To find the power (P) delivered to the object, we need to determine the work done (W) per unit time (t). Since the object is moving at a constant velocity, we know that the net force is zero since there is no acceleration.
The work done can be calculated using the formula W = Fd, where F is the force applied and d is the distance over which the force acts. In this case, since the velocity is constant, we consider displacement (d) as the distance traveled over time (t).
Since the object is moving at a constant velocity, we can say that the force applied is equal to the resistive force acting in the opposite direction. Therefore, F = 15 N.
Using the formula for work, W = Fd, and rearranging the formula to solve for displacement (d), we have d = W/F.
Substituting the values, we have:
d = W/15 N
Since the object is moving at a constant velocity, we can calculate the displacement (d) using the formula d = vt, where v is the velocity and t is the time taken to travel the distance. In this case, we don't have the time taken, but we can calculate it by dividing the displacement (d) by the velocity (v).
Substituting the values, we have:
t = d/v
Now, we have the expression for time (t) in terms of displacement (d) and velocity (v).
Since we know that the net force is zero, we can calculate the work done by substituting the expression for time (t) into the equation for work, W = Fd.
Substituting the values, we have:
W = 15 N × d/v
Finally, we can substitute the expression for work (W) into the power formula, P = W/t.
Substituting the values, we have:
P = (15 N × d/v) / (d/v)
Simplifying the expression, we find:
P = 15 N
Therefore, the power required to deliver to the object is 15 watts (W).
To solve this problem, you can use the equation for power: P = W / t, where P is power, W is work, and t is time. You already correctly identified that work can be calculated using the equation W = Fd, where F is the force and d is the distance.
In this case, we are given the force F = 15 N and the velocity v = 5 m/s. To find the work, we need to know the distance the object is moved. However, since the object is moving at a constant velocity, we can use the equation v = d / t, where d is the distance and t is the time. Rearranging the equation, we get d = v * t.
Now, we can substitute the values into the equations to find the work and power. The work is given by W = Fd, so W = (15 N)(5 m/s)(t), and the power is given by P = W / t, so P = (15 N)(5 m/s)(t) / t. Simplifying this equation, we get P = (15 N)(5 m/s).
Therefore, the power that must be delivered to the object by the force is 75 Watts (Joules per second)