The cart is at rest, so it is in equilibrium and there is no net force acting on it. The only forces acting on the cart are its weight (magnitude <em>w</em>), the normal force (mag. <em>n</em>), and the friction force (maximum mag. <em>f</em> ).
In the horizontal direction, we have
<em>n</em> cos(120º) + <em>f</em> cos(30º) = 0
-1/2 <em>n</em> + √3/2 <em>f</em> = 0
<em>n</em> = √3 <em>f</em>
and in the vertical,
<em>n</em> sin(120º) + <em>f</em> sin(30º) + (-<em>w</em>) = 0
<em>n</em> sin(120º) + <em>f</em> sin(30º) = (50 kg) (9.80 m/s²)
√3/2 <em>n</em> + 1/2 <em>f</em> = 490 N
Substitute <em>n</em> = √3 <em>f</em> and solve for <em>f</em> :
√3/2 (√3 <em>f </em>) + 1/2 <em>f</em> = 490 N
2 <em>f</em> = 490 N
<em>f</em> = 245 N
(pointed up the incline)
Answer:
Length (l) = 6 m
height (h) = 3 m
Load(L) = 500 N
Effort (E) = ?
we know the principal that
E * l = L * h
6 E = 500 * 3
6E = 1500
E = 250
therefore 250 N work is done on the barrel.
Answer:
A. Ein = 8.05*10^-4 V/m
B. Clockwise sense
Explanation:
A. the magnitude of the electric field induced in the ring is obtaind by using the following formula:
(1)
Ein: induced electric field
ds: differential of a path of the ring
ФB: magnetic flux in the ring
The Ein vector is parallel to ds in the complete ring. Furthermore, the area of the ring is constant, hence, you have in the equation (1):
(2)
dB/dt = -0.280T/s (it is decreasing)
A: area of the ring = π(r/2)^2= (π/4) r^2
r: radius of the ring = 4.60/2 = 2.30 cm
Then, you replace the values of all variables in the equation (2):
hence, the induced electric field is 8.05*10^-4 V/m
B. The induced current in the ring produced a magnetic field that is opposite to the magnetic field of the magnet. The, in this case you have that the induced current is in a clockwise sense.
At a given moment in time, the instantaneous speed can be thought of as the magnitude of instantaneous velocity.
Instantaneous speed is the magnitude of the instantaneous velocity, the instantaneous velocity has direction but the instantaneous speed does not have any direction. Hence, the instantaneous speed has the same value as that of the magnitude of the instantaneous velocity. It doesn't have any direction.
Explanation:
The formula for KE ( Kinetic Energy ) is : 1/2 mv²
Solution:
- First we solve for v ( velocity ) using the formula 2gh, where g is gravity [ 9.8 m/s² ] and h is height [ 1.25 m ]
= 2 ( 9.8 m/s² × 1.25 m ) = 24.5 m/s
- The velocity is 24.5 m/s.
- Now solve for KE using the formula 1/2 mv²
= 1/2 ( 40 kg × 24.5m/s ² )
= 1/2 ( 40 kg × 600.25 )
= 1/2 ( 24,010 )
= 12,005 Joules
- The diver's kinetic energy is 12,005 J.
