Explanation:
The position vector r:

The velocity vector v:

The acceleration vector a:



Answer:(a)891.64 N
(b)0.7
Explanation:
Mass of crate 
Crate slows down in 
initial speed 
inclination 
From Work-Energy Principle
Work done by all the Forces is equal to change in Kinetic Energy




change in kinetic energy

(b)Coefficient of sliding friction



and 


Answer:
(i) 208 cm from the pivot
(ii) Move further from the pivot
Explanation:
(i) Sum of the moments about the pivot of the seesaw is zero.
∑τ = Iα
(50 kg) (10 N/kg) (2.5 m) + (60 kg) (10 N/kg) x = 0
1250 Nm + 600 N x = 0
x = -2.08 m
Kenny should sit 208 cm on the other side of the pivot.
(ii) To increase the torque, Kenny should move away from the pivot.
Answer:
a) The sign of the charge is positive.
b) The magnetic force on the particle is 0.050 newtons.
Explanation:
The magnetic force F on a moving charge with velocity v passing through a magnetic field B is:
(1)
a)
Because it is a cross product, we can find the direction of the force using the right-hand rule, that is too the direction of the movement. We have two possibilities here because the velocity vector and magnetic field are perpendicular: the particle deflects towards east or toward west, which depends on the charge of the particle. Note that if you put your right hand fingers, except thumb, pointing towards north (direction of velocity) and later close them in the direction of the magnetic field, if you maintain your thumb perpendicular to this movement it will point towards east (See figure), so that will be de direction of the force if the charge is positive, but if the charge is negative, the direction will be opposite (towards west). So the charge has to be positive to deflects towards east.
b)
Now by 1:
