A 100-g toy car is propelled by a compressed spring that starts it
moving. The car follows the curved track Show that the final speed of the toy car is 0.687 m/s if its initial speed is 2.00 m/s and it coasts up the frictionless slope, gaining 0.180 m in altitude
use conservation of Mechanical energy formula.
change in ME=0
change in Ek+change in PE=0
1/2mvf^2+mghf=1/2mvi^2 +mghi
1/2(0.100)(0.687)^2+(0.100)(9.81)(0.180)=1/2(0.100)(2.00)^2+(0.100)(9.81)(0)
0.20=0.20
To find the final speed of the toy car, we can use the principle of conservation of mechanical energy. The total mechanical energy of the car remains constant throughout its motion.
The total mechanical energy can be calculated as the sum of the kinetic energy (KE) and potential energy (PE).
In this case, we can consider the initial speed of 2.00 m/s as the kinetic energy and the gain in altitude of 0.180 m as the potential energy.
Given:
Initial speed (kinetic energy) = 2.00 m/s
Gain in altitude (potential energy) = 0.180 m
Step 1: Calculate the initial total mechanical energy (E_initial):
E_initial = KE_initial + PE_initial
E_initial = (1/2)mv^2 + mgh
where m is the mass of the toy car, v is the initial speed, g is the acceleration due to gravity, and h is the gain in altitude.
Since the toy car is moving up a slope, we need to consider the change in height as positive, so h = +0.180 m.
Assuming the mass of the car is 100 g (0.100 kg):
E_initial = (1/2)(0.100 kg)(2.00 m/s)^2 + (0.100 kg)(9.81 m/s^2)(+0.180 m)
Step 2: Calculate the final total mechanical energy (E_final):
Since there is no friction, the final speed of the toy car will be due to the conversion of potential energy to kinetic energy, so the gain in altitude becomes negative:
h = -0.180 m
E_final = KE_final + PE_final
E_final = (1/2)mv^2 + mgh
Since the final speed is given as 0.687 m/s, we can substitute this value for v:
E_final = (1/2)(0.100 kg)(0.687 m/s)^2 + (0.100 kg)(9.81 m/s^2)(-0.180 m)
Step 3: Calculate the final speed (v_final):
E_initial = E_final (due to the conservation of mechanical energy)
Solve the equation for v_final.
(1/2)(0.100 kg)(2.00 m/s)^2 + (0.100 kg)(9.81 m/s^2)(+0.180 m) = (1/2)(0.100 kg)(0.687 m/s)^2 + (0.100 kg)(9.81 m/s^2)(-0.180 m)
Now, rearrange and solve for v_final:
(1/2)(0.100 kg)(0.687 m/s)^2 = (1/2)(0.100 kg)(2.00 m/s)^2 + (0.100 kg)(9.81 m/s^2)(+0.180 m) - (0.100 kg)(9.81 m/s^2)(-0.180 m)
Simplify the equation and solve for v_final.
By following these steps, you will be able to calculate the final speed of the toy car.
dfd
hsd
vf^2=vi^2 + 2gd
g=-9.8m/s^2, d=.180 m, vi given. mass is not needed.