An asteroid is moving along a straight line. A force acts along the displacement of the asteroid and slows it down. The asteroid has a mass of 4.9 × 104 kg, and the force causes its speed to change from 7600 to 5400 m/s. (a) What is the work done by the force? (b) If the asteroid slows down over a distance of 1.9 × 106 m determine the magnitude of the force.
i found the work is -7.007E11 but i cant find part b) magnitude of the force
Force*distance=workdone
but distance=1.9E6m
solve for force.
force will be -7.007E11/1.9E6 then?
To find the magnitude of the force acting on the asteroid, we can use the work-energy principle. The work done by the force is equal to the change in kinetic energy of the asteroid.
Given:
Mass of the asteroid (m) = 4.9 × 10^4 kg
Initial velocity (v1) = 7600 m/s
Final velocity (v2) = 5400 m/s
Distance over which the asteroid slows down (d) = 1.9 × 10^6 m
(a) Work done by the force:
The work done by the force can be calculated using the equation:
Work (W) = change in kinetic energy (ΔKE)
The change in kinetic energy is given by:
ΔKE = (1/2) * m * (v2^2 - v1^2)
Substituting the given values:
ΔKE = (1/2) * (4.9 × 10^4 kg) * ((5400 m/s)^2 - (7600 m/s)^2)
ΔKE = (1/2) * (4.9 × 10^4 kg) * (-3.086 × 10^7 m^2/s^2)
ΔKE = -7.5904 × 10^12 J
Therefore, the work done by the force is -7.5904 × 10^12 J.
(b) Magnitude of the force:
The magnitude of the force can be calculated using the equation:
Work (W) = force (F) * distance (d)
Rearranging the equation, we can solve for the force:
F = W / d
Substituting the values:
F = (-7.5904 × 10^12 J) / (1.9 × 10^6 m)
F = -3.9947 × 10^6 N
Therefore, the magnitude of the force acting on the asteroid is approximately 3.9947 × 10^6 N. Note that the negative sign indicates that the force is acting in the opposite direction of the asteroid's motion.
To find the magnitude of the force in part b), we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. The work done by the force can be calculated by multiplying the force by the distance over which it acts. In this case, the force is acting in the opposite direction of the motion, so we need to consider the negative sign.
Let's begin by calculating the work done by the force using the work-energy theorem:
Work done by the force (W) = Change in kinetic energy
The change in kinetic energy (ΔKE) can be calculated as:
ΔKE = KE_final - KE_initial
Given that the initial velocity (v_initial) is 7600 m/s and the final velocity (v_final) is 5400 m/s, we can calculate the change in kinetic energy:
ΔKE = (1/2) * m * (v_final^2 - v_initial^2)
Using the given mass (m) of 4.9 × 10^4 kg, we can substitute the values and calculate ΔKE:
ΔKE = (1/2) * 4.9 × 10^4 kg * ((5400 m/s)^2 - (7600 m/s)^2)
Calculating this equation gives us a value of -7.007 × 10^11 Joules, which matches your result for part a).
Next, to determine the magnitude of the force, we can use the equation for work:
Work (W) = Force (F) * Distance (d)
Since we already know the work done by the force (-7.007 × 10^11 J) and the distance (1.9 × 10^6 m), we can rearrange the equation to solve for the force:
F = W / d
Substituting the values, we get:
F = (-7.007 × 10^11 J) / (1.9 × 10^6 m)
Evaluating this equation gives us the magnitude of the force, which is approximately -3.68 × 10^5 Newtons. Note that the negative sign indicates that the force is acting in the opposite direction of the motion.