Answer:
option c
Explanation:
Kinetic energy is due to the speed of a body.
When speed is doubled, the kinetic energy is quadruple.
From third equation of motion, braking distance is also proportional to square of speed. Thus, when speed is doubled, the braking distance is quadruple.
Thus, option c is correct.
1) X-component: 568.5 N, Y-component: 511.9 N
2) The horizontal force is 86.6 N and the resulting acceleration is
Explanation:
1)
In this first part of the problem, we have to resolve the force into its two components, along the x and the y direction.
The two components are given by:
where
F = 765 N is the magnitude of the force
is the angle of the force with the horizontal
Substituting, we find:
2)
First of all, we have to find the horizontal component of the pulling force, which is given by
where
F = 100 N is the magnitude of the pulling force
is the direction of the force with the horizontal
Substituting,
Now we can find the acceleration of the wagon by using Newton's second law:
where
is the net force in the horizontal direction
m = 100 kg is the mass of the wagon
is the acceleration in the horizontal direction
Solving for , we find
Learn more about vector components:
And about Newton's second law:
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(a) 4.0 s
The acceleration of the car is given by
where
v is the final velocity
u is the initial velocity
t is the time interval
For this car, we have
v = 0 (the final speed is zero since the car comes to a stop)
u = 20 m/s is the initial velocity
is the deceleration of the car
Solving the equation for t, we find the time needed to stop the car:
(b) 40 m
The stopping distance of the car can be calculated by using the equation
where
v = 0 is the final velocity
u = 20 m/s is the initial velocity
a = -5.0 m/s^2 is the acceleration of the car
d is the stopping distance
Solving the equation for d, we find
(c)
The deceleration is given by the problem, and its value is .
(d) 5000 N
The net force applied on the car is given by
where
m is the mass of the car
a is the magnitude of the acceleration
For this car, we have
m = 1000 kg is the mass
is the magnitude of the acceleration
Solving the formula, we find
(e)
The work done by the force applied by the car is
where
F is the force applied
d is the total distance covered
Here we have
F = 5000 N
d = 40 m (stopping distance)
So, the work done is
(f) The kinetic energy is converted into thermal energy
Explanation:
when the breaks are applied, the wheels stop rotating. The car slows down, as a result of the frictional forces between the brakes and the tires and between the tires and the road. Due to the presence of these frictional forces, the kinetic energy is converted into thermal energy/heat, until the kinetic energy of the car becomes zero (this occurs when the car comes to a stop, when v = 0).