Answer:
75 N
Explanation:
In this problem, the position of the crate at time t is given by
[tex]y(t)=2.80t+0.61t^3[/tex]
The velocity of the crate vs time is given by the derivative of the position, so it is:
[tex]v(t)=y'(t)=\frac{d}{dt}(2.80t+0.61t^3)=2.80+1.83t^2[/tex]
Similarly, the acceleration of the crate vs time is given by the derivative of the velocity, so it is:
[tex]a(t)=v'(t)=\frac{d}{dt}(2.80+1.83t^2)=3.66t[/tex] [m/s^2]
According to Newton's second law of motion, the force acting on the crate is equal to the product between mass and acceleration, so:
[tex]F(t)=ma(t)[/tex]
where
m = 5.00 kg is the mass of the crate
At t = 4.10 s, the acceleration of the crate is
[tex]a(4.10)=3.66\cdot 4.10 =15.0 m/s^2[/tex]
And therefore, the force on the crate is:
[tex]F=ma=(5.00)(15.0)=75 N[/tex]
