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(a) Show that tans = 2
(b) Find the magnitude of the reaction force at the wall and on the ground.
(a) Calculate the resistance R to the motion of the car if the road is horizontal.
Given that R is proportional to the square of the speed of the car,
(b) Show that R = 9v^2 /2 .
A small is eating dinner on a flat table that is 1 meter tall. When asked to eat his vegetables, the child pushes his plate away from him at a speed of 4 m/s. Due to friction, the plate decelerates at a constant rate of 1 m/s2. After 1 second, the plate falls off the edge of the table.
a. How far did the plate travel over the 1 second?
b. What is the speed of the plate at the instant it falls off the table?
c. How much time will pass between the instant the plate leaves the table and the instant it reaches the ground?
d. At what speed will the plate strike the ground?
e. At what angle will the plate strike the ground?
Consider two vectors A and B. Vector A has a magnitude of 13 and points at an angle of 72 degrees above the +x axis. Vector B has a magnitude of 8 and points at an angle of 31 degrees below the +x axis.
a. What are the x and y components of vector A?
b. What are the x and y components of vector B?
c. Suppose vector C is defined as C=A+B. What are the x and y components of vector C?
d. What is the magnitude of vector C?
e. At what angle does vector C point?
A box of mass m=15 kg at the packaging section of a factory comes to the top of a ramp ("\\theta =37^{\\circ }") with speed vo and slides down where it is picked up for shipment. In order to avoid damage to the box a spring is used with force constant k=100N/m and the maximum force Fmax=100N. The box slides a distance of l=4 m down the incline before it hits the spring as shown. The coefficient of kinetic friction between the box and entire ramp is 0.75.
a) Find the work done by the gravity , normal force and friction force on the box until it hits the spring.
b) Find the maximum speed of the box at the top of the ramp if the box is to be picked up when the spring is in maximum compression.
- A bullet leaves the barrel of a gun at a speed of 220 m/s at an angle of 10 degrees above the horizontal. At the moment the bullet leaves the barrel, the acceleration of the bullet is:
- 0
- 220 m/s2 to the right
- 9.8 m/s2 upward
- 9.8 m/s2 downward
A spaceship of mass m has velocity v in the positive x direction of an inertial reference frame. A mass dm is fired out the rear of the ship with constant exhaust velocity (-v0) with respect to the spaceship. a) using conservation of momentum, show that dv/v0 = dm/m, b) By integration, find the dependence of v on m if v1 and m1 are the initial values. c) Can the acceleration be constant if dm/dt, the burning rate is constant.
A gas molecule having a speed of 300 m/sec collides elastically with another molecule of same mass which is initially at rest. After the collision the first molecule moves at an angle of 30 degree to its initial direction. Find the speed of each molecule after collision and the angle made with the incident direction by the recoiling target molecule.
A train starts from a rest from a station and start with uniform acceleration 0.5m/s^2 for 20 seconds. It travels with uniform velocity for 30s. The break are then applied so that a uniform retardation is obtained and the train comes to rest in a further 10 seconds. Sketch the velocity time graphy of this motion
Differential between dynamics of system of particles and that of rigid
body.
