Answer:
6.62s
Explanation:
Metric unit conversion:
364 g = 0.364 kg
789 g = 0.789 kg
Starting from rest, the cart takes 4.49 s to travel a distance of 1.43 m. We can use the following equation of motion to calculate the constant acceleration
[tex]s = a_1t_1^2/2[/tex]
[tex]a_1 = \frac{2s}{t_1^2} = \frac{2*1.43}{4.49^2} = 0.142 m/s^2[/tex]
Using Newton's 2nd law, we can calculate the force generated by the fan to push the 0.364 kg cart forward
[tex]F = a_1m_1 = 0.142*0.364 = 0.052 N[/tex]
Now that more mass is added, the new acceleration of the 0.789 kg cart is
[tex]a_2 = F/m_2 = 0.052 / 0.789 = 0.065 m/s^2[/tex]
We can reuse the same equation of motion to calculate the time it takes to travel 1.43 m from rest
[tex]s = a_2t_2^2/2[/tex]
[tex]t_2^2 = 2s/a_2 = 2*1.43/0.065 = 43.7[/tex]
[tex]t_2 = \sqrt{43.7} = 6.62s[/tex]
Answer:
6.32 s.
Explanation:
Given:
Mass of cart = 364 g
= 0.364 kg
Mass of cart with added mass = 789 g
= 0.789 kg.
Using equations of motion;
S = ut + 1/2 * at^2
S = a * t^2/2
1.43 = (a * 4.29^2)/2
= 0.155 m/s^2
F = m * a
= 0.364 * 0.155
= 0.0564 N
Acceleration, a2 of the new mass combination = F/m2
= 0.0564/0.789
= 0.0715 m/s^2
Calculating the new time, t2;
S = a * t2^2/2
1.43 = (0.0715 * t2^2)/2
t2^2 = 40
t2 = sqrt(40)
= 6.32 s.
= 0.155 m/s^2
