[Q 4] (a) The equation of a hill path is given by: Y = -0.001 x + 0.2 x A small vehicle of mass 80 Kg starts from rest at the bottom of hill (point (0,0)) and accelerated toward the top of hill. Find maximum allowable acceleration to keep the vehicle in contact with the surface when reaching top of hill.
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- A parachutist whose mass is 75 kg drops from a helicopter hovering 1000 m above the ground and falls toward the ground under the influence of gravity. Assume that the force due to air resistance is proportional to the velocity of the parachutist, with the proportionality constant b, 30 N-secim when the chute is closed and by 100 N-secim when the chule is open if the chute does not open until the velocity of the parachutist reaches 20 m/sec, after how many seconds will the parachutist reach the ground? Assume that the acceleration due to gravity is 9.81 m/sec The parachutist will reach the ground after (Round to two decimal places as needed.) seconds. CHE1) In Figure, a block with mass m = 1 kg is released from height h, friction until it reaches the path with first length d,= 3 m, where the friction force between B and C is f, = 9 N, and until it reaches the path, where the friction force between E and F is f, = 7 N. The height is h, = 1 m, and second horizontal length is d,= 1 m. The block continues its motion after the point F. (a) Find the velocity at the point A. (b) Find the velocity at the point D. (c) Find the height h if the velocity of m is v= 9 m/s at the point F.(sin45=0.7 g=9.8 m/s²) 11 m. Its path is without 1 m (F d,=1 m h h, = 11 m D 45° E d,=3 m h,=1 m A ВNeglecting friction and air resistance, a car with an initial velocity of 76.5 km/h coasts up a hill and comes to stop at the hill's top. What must be the height of the hill (in meters)
- 1. Given that sinθ = 2/3 and cosθ = √5/3, find the cotθ, and tanθ. 2. To move a large crate across a rough floor, you push on it with a force F at an angle of 21° below the horizontal, as shown in Figure 6–18. Find the force necessary to start the crate moving, given that the mass of the crate is 32 kg and the coefficient of static friction between the crate and the floor is 0.57. Find the acceleration of the crate if the applied force is 330 N and the coefficient of kinetic friction is 0.45.3) A block starts from rest. It is pushed with an applied force for d, m. It is released and travels over a rough patch. Calculate the maximum vertical displacement up the incline. F. ///\ 0 = *ri •'p d,, H = 0.2 d, = 10 m d2 = 3 m |F.| = 100 N 10 kg e = 30° m =Problem 3: Incline with Friction |A mass m = 2 kg is launched with an initial speed vo = 1 m/s down an incline with coefficient of static friction H, = 3/4 and coefficient of kinetic friction A = 2/3. It travels a distance L = 4 m down the incline before reaching the bottom of the incline with speed vy. The angle 0 such that the values of cos(8) and sin(0) are the ones provided below and you may use g = 10 m/s².
- (b) A frictionless incline is 5.00 m long (the distance from the top of the incline to the bottom, measured along the incline). The vertical distance from the top of the incline to the bottom is 1.66 m. A small block is released from rest at the top of the incline and slides down the incline. (i) How long does it take the block to reach the ground? 3.25 s (ii) What is the speed of the block just before it strikes the ground? 1.75 m/sA frictionless plane is 10.0 m long and inclined at 35.0°.A sled starts at the bottom with an initial speed of 5.00 m/sup the incline. When the sled reaches the point at which itmomentarily stops, a second sled is released from the top ofthe incline with an initial speed vi. Both sleds reach the bottomof the incline at the same moment. (a) Determine the distance that the first sled traveled up the incline. (b) Determinethe initial speed of the second sled.At an accident scene on a level road, investigators measure a car’s skid mark to be 85 m long. It was a rainy day and the coefficient of friction was estimated to be 0.37. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. (round to the nearest tenth)
- At an accident scene on a level road, investigators measure a car’s skid mark to be 112 m long. It was a rainy day and the coefficient of friction was estimated to be 0.42. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes.Three youths push a 40.0-kg block of ice so that it begins to coast on a frozen lake. With an initial speed Vi of 3.00 m/s, the block of ice now moves up an icy ramp at the edge of the lake. Neglecting air resistance and in the absence of any friction between the ice block and the frozen lake and ramp, use the CMEP to calculate how high up the ramp (h in the figure) the block of ice moves before stopping. As a suggestion, use the base of the ramp as GZ. 0.204 m 0.625 m 0.459 m 0.511 m 0.165 m 0.270 m O O OAn 8 kg block is shot up an incline of 300with an initial speed of 3.6 m/s. How far up the incline will the block travel if the coefficient of friction between it and the incline is 0.22? Hint: Express the height above the ground that the block is above the incline in terms of the distance up the incline (hypotenuse).