A car of mass 1100kg stands on an incline of 8 degrees. If the hand brake is released, what will be the velocity of the car after travelling 80 m if the resistance to motion is equal to 170 N
To find the velocity of the car after traveling a certain distance, we can use the equations of motion. The key is to break down the forces acting on the car and use those to determine the acceleration.
Step 1: Determine the vertical and horizontal components of the weight of the car.
The weight of the car can be broken down into two components: one perpendicular to the incline and one parallel to the incline.
The perpendicular component is equal to mg * cosθ, where m is the mass of the car (1100 kg) and θ is the angle of the incline (8 degrees).
The horizontal component is equal to mg * sinθ.
Step 2: Determine the net force acting on the car parallel to the incline.
The net force is the difference between the force of gravity parallel to the incline and the resistance to motion: Fnet = mg * sinθ - R, where R is the resistance to motion (170 N).
Step 3: Determine the acceleration of the car.
Using Newton's second law, Fnet = ma, where Fnet is the net force and m is the mass of the car, we can rearrange the equation to find the acceleration: a = Fnet / m.
Step 4: Determine the time it takes for the car to travel 80 m.
We can use the kinematic equation: s = ut + 0.5at^2, where s is the distance traveled, u is the initial velocity (0 in this case), a is the acceleration, and t is the time.
Step 5: Determine the final velocity of the car using the equation v = u + at.
Given that the initial velocity (u) is 0, the equation simplifies to v = at.
Let's calculate the values:
Step 1:
Perpendicular component: mg * cosθ = 1100 kg * 9.8 m/s^2 * cos(8 degrees) = 1042.4 N
Horizontal component: mg * sinθ = 1100 kg * 9.8 m/s^2 * sin(8 degrees) = 152.9 N
Step 2:
Net force = 152.9 N - 170 N = -17.1 N (negative because the force opposes the motion)
Step 3:
Acceleration = (-17.1 N) / 1100 kg = -0.0155 m/s^2
Step 4:
s = 80 m
u = 0 m/s
Using the equation s = ut + 0.5at^2, we can rearrange to solve for t:
80 m = 0.5 * (-0.0155 m/s^2) * t^2
160 m = (-0.0155 m/s^2) * t^2
t^2 = 160 m / (-0.0155 m/s^2)
t ≈ √(10322.58 s^2)
t ≈ 101.6 s
Step 5:
v = at
v = (-0.0155 m/s^2) * 101.6 s
v ≈ -1.57 m/s
Thus, the velocity of the car after traveling 80 m will be approximately -1.57 m/s. The negative sign indicates that the car is moving in the opposite direction of the incline.